Analysis of a post-fracture pressure buildup test with wellbore-storage distortion


\(q_{g}\): Gas flow rate (MSCF/day)

\(B_{g}\): Gas formation Volume Factor (RB/MSCF)

\(p_{D}\): Dimensionless Pressure (dimensionless)

\(\varnothing\): Porosity (dimensionless)

\(c_{t}\): Compressibility \((1 / \mathrm{psi})\)

\(\mu\): Viscosity \((\mathrm{cP})\)

\(\mathrm{h}\): Formation Thickness (ft)

\(t_{\left(L_{\rangle_{D}}\right.}\): Time of end of linear or pseudo radial flow from plot (dimensionless)

\(C_{r D}\): Dimensionless fracture conductivity (dimensionless)

\(C_{f D}\): Dimensionless Wellbore storage coefficient (dimensionless)

\(L_{f}\): Length of fracture \((\mathrm{ft})\)

\(\mathrm{k}\): Permeability \((\mathrm{mD})\)

\(\Delta t_{A E}\): Equivalent Adjusted delta time from derivative curve (h)


C: Well bore storage coefficient (bbl/psi)

\(w_{f k_{f}}\): Min Fracture conductivity for infinite conductive fracture \((\mathrm{mD} \mathrm{ft})\)

\(L_{f M P}\): Length of fracture from match point analysis (ft)

\(\left(\Delta P_{a}\right)_{M P}\): Adjusted Pressure difference at match point from plot (psi)


\[ \begin{gathered} C=\left(141.2 * q_{g} * B_{g} * \frac{\mu}{k * h}\right) *\left(p_{D}\right)_{M P} \\ w_{f k_{f}}=\left(\left(\frac{0.0002637 * k}{\varnothing * \mu * c_{t}}\right) *\left(\frac{\Delta t_{A E}}{t_{\left(L_{f}\right)_{D}}}\right)_{M P}\right)^{\frac{1}{2}} \\ L_{f M P}=\left(\emptyset * h * c_{t} * \frac{L_{f}^{2}}{0.8936}\right) * C_{f D} \\ \left(\Delta P_{a}\right)_{M P}=3.14 * k * C_{r D} * L_{f} \end{gathered} \]


Lee, J., Rollins J.B., and Spivey J.P. 2003, Pressure Transient Testing, Vol. 9, SPE Textbook Series, Vol. 9 , Henry L. Doherty Memorial Fund of AIME, Richardson, Texas, SPE, Chapter: 6, Page: 127.


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